The VAE is a maximum likelihood estimator that approximates the evidence by maximizing the evidence lower bound [1]}. The core problem with this approach lies in the approximation of the posterior. In achieving a closed form solution, one must know a-priori the posterior's functional form. The standard approach assumes a gaussian, as such it performs poorly on multimodal or non-gaussian data. Alternative posteriors have been proposed in the literature [2]}, but these methods still require a-priori knowledge of the posterior's functional form.
